The Chomsky Hierarchy Costas Busch - LSU

Linear-Bounded Automata: Same as Turing Machines with one difference: the input string tape space is the only tape space allowed to use Costas Busch - LSU

Linear Bounded Automaton (LBA) Input string Working space in tape Left-end marker Right-end marker All computation is done between end markers Costas Busch - LSU

We define LBA’s as NonDeterministic Open Problem: NonDeterministic LBA’s have same power as Deterministic LBA’s ? Costas Busch - LSU

Example languages accepted by LBAs: LBA’s have more power than PDA’s (pushdown automata) LBA’s have less power than Turing Machines Costas Busch - LSU

Unrestricted Grammars: Productions String of variables and terminals String of variables and terminals Costas Busch - LSU

Example unrestricted grammar: Costas Busch - LSU

Theorem: A language is Turing-Acceptable if and only if is generated by an unrestricted grammar Costas Busch - LSU

Context-Sensitive Grammars: Productions String of variables and terminals String of variables and terminals and: Costas Busch - LSU

is context-sensitive: The language is context-sensitive: Costas Busch - LSU

A language is context sensistive if and only if Theorem: A language is context sensistive if and only if it is accepted by a Linear-Bounded automaton Observation: There is a language which is context-sensitive but not decidable Costas Busch - LSU

Non Turing-Acceptable The Chomsky Hierarchy Non Turing-Acceptable Turing-Acceptable decidable Context-sensitive Context-free Regular Costas Busch - LSU